Question

Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3? inches, with a standard deviation of

2.62.6

inches. A baseball analyst wonders whether the standard deviation of heights of? major-league baseball players is less than

2.62.6

inches. The heights? (in inches) of

2020

randomly selected players are shown in the table.

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Click the icon to view the data table.

Test the notion at the

alpha equals 0.10?=0.10

level of significance.

What are the correct hypotheses for this? test?

The null hypothesis is

H0?:

?

sigma?

mu?

pp

?

not equals?

equals=

greater than>

less than<

2.62.6.The alternative hypothesis is

H1?:

?

pp

mu?

sigma?

?

greater than>

not equals?

less than<

equals=

2.62.6.

Calculate the value of the test statistic.

chi Subscript Superscript 2?2 equals=nothing

?(Round to three decimal places as? needed.)

Use technology to determine the? P-value for the test statistic.

The? P-value is

nothing.

?(Round to three decimal places as? needed.)

What is the correct conclusion at the

alpha equals 0.10?=0.10

level of? significance?Since the? P-value is

?

less

greater

than the level of? significance,

?

do not reject

reject

the null hypothesis. There

?

is

is not

sufficient evidence to conclude that the standard deviation of heights of? major-league baseball players is less for? major-league baseball players at the

0.100.10

level of significance.

72	70	77	74
74	77	73	75
71	75	75	73
71	72	70	74
76	72	73	74

Answer 1

The null hypothesis is : H0?: ? =2.6

The alternative hypothesis is H1: ? <2.6

here test statistic ?2 =(n-1)s²/?² =(20-1)*2.088²/2.6² =12.254 ( please try 12.277 if this comes wrong)

p value =0.126 ( please try 0.127 if this comes wrong)

Since the? P-value is greater than the level of? significance do not reject the null hypothesis. There is not sufficient evidence to conclude that the standard deviation of heights of? major-league baseball players is less for? major-league baseball players at the 0.10 level of significance.